Summation of slowly convergent series by Gaussian type of quadratures and application to calculation of values of the Riemann zeta function
Konferencijski prilog (Objavljena verzija)
Metapodaci
Prikaz svih podataka o dokumentuApstrakt
Beside a short account on the summation/integration methods for slowly
convergent series (Laplace transform method for numerical and trigonometric series and the
method of contour integration over a rectangle), a method based on a new transformation of
the series to a weighted integral, with respect to the weight function
over R+, is presented. Such a method is applied to calculation of the values of the Riemann
zeta function. Several numerical examples are included.
Ključne reči:
Slowly convergent series / Gaussian quadrature / weight function / three-term recurrence relation / convergence / Laplace transform / contour integration / Riemann zeta functionIzvor:
Bulletin T.CLIV de l’Académie serbe des sciences et des arts, 2021, 131-150Izdavač:
- Beograd : Académie Serbe des sciences et des arts
Napomena:
- Bulletin t. 154 de l'Académie serbe des sciences et des arts. Classe des sciences mathématiques et naturelles. Sciences mathematiques no 46
TY - CONF AU - Milovanović, Gradimir V. PY - 2021 UR - https://dais.sanu.ac.rs/123456789/13287 AB - Beside a short account on the summation/integration methods for slowly convergent series (Laplace transform method for numerical and trigonometric series and the method of contour integration over a rectangle), a method based on a new transformation of the series to a weighted integral, with respect to the weight function over R+, is presented. Such a method is applied to calculation of the values of the Riemann zeta function. Several numerical examples are included. PB - Beograd : Académie Serbe des sciences et des arts C3 - Bulletin T.CLIV de l’Académie serbe des sciences et des arts T1 - Summation of slowly convergent series by Gaussian type of quadratures and application to calculation of values of the Riemann zeta function SP - 131 EP - 150 UR - https://hdl.handle.net/21.15107/rcub_dais_13287 ER -
@conference{ author = "Milovanović, Gradimir V.", year = "2021", abstract = "Beside a short account on the summation/integration methods for slowly convergent series (Laplace transform method for numerical and trigonometric series and the method of contour integration over a rectangle), a method based on a new transformation of the series to a weighted integral, with respect to the weight function over R+, is presented. Such a method is applied to calculation of the values of the Riemann zeta function. Several numerical examples are included.", publisher = "Beograd : Académie Serbe des sciences et des arts", journal = "Bulletin T.CLIV de l’Académie serbe des sciences et des arts", title = "Summation of slowly convergent series by Gaussian type of quadratures and application to calculation of values of the Riemann zeta function", pages = "131-150", url = "https://hdl.handle.net/21.15107/rcub_dais_13287" }
Milovanović, G. V.. (2021). Summation of slowly convergent series by Gaussian type of quadratures and application to calculation of values of the Riemann zeta function. in Bulletin T.CLIV de l’Académie serbe des sciences et des arts Beograd : Académie Serbe des sciences et des arts., 131-150. https://hdl.handle.net/21.15107/rcub_dais_13287
Milovanović GV. Summation of slowly convergent series by Gaussian type of quadratures and application to calculation of values of the Riemann zeta function. in Bulletin T.CLIV de l’Académie serbe des sciences et des arts. 2021;:131-150. https://hdl.handle.net/21.15107/rcub_dais_13287 .
Milovanović, Gradimir V., "Summation of slowly convergent series by Gaussian type of quadratures and application to calculation of values of the Riemann zeta function" in Bulletin T.CLIV de l’Académie serbe des sciences et des arts (2021):131-150, https://hdl.handle.net/21.15107/rcub_dais_13287 .